Question

short form of 8 power minus 1 by 3​

Answer 1

Question :-

${(8) } ^{ \frac{ - 1}{3} }$

Answer :-

$\implies \frac{1}{{8}^{ \frac{1}{3} } } \\ \\ \implies \frac{1}{ {2}^{ {3}^{ \frac{1}{3} } } } \\ \\ \implies \frac{1}{2} \\ \\ \implies \: 0.5$

We should Understand, how did we do it from starting

Firstly we did the Reciprocal of the number, as it is negative.

Then, We broke 8 into $2^3$

Also, $\dfrac{1}{ (2^3)^{\frac{1}{3}} }$ which converts it into root that is $\dfrac{1}{\sqrt[3]{8} }$

Which would give $\frac{1}{2}$ and we can write it as 0.5

Additional Information:-

Indices:

1. The power of any real number is known as its index.

For example, 2² = 4.

Here, the index of 2 is 2 and of 4 is 1

2. Use of indices:

Indices are mainly used to describe either big numbers ( weight of planets, sun) or small numbers and amounts ( the weight of an atom, electron).

3. Rules of indices:

1. a^m × a^n = a^m + n

2. a^m ÷ a^n = a^m - n ( m > n )

3. a^m ÷ a^n = a^n - m ( n > m )

4. (a^m)^n = a^m × n

5. a^0 = 1

The index of 2² is read as square of 2.

The index of 2³ is read as cube of 3.

The index of 2⁴ is read as 2 raised to 4 or 2 to the power of 4.

Answer 2

Answer

As per your question you need short form of $\rm 8^ \frac { -1 } { 3 }$

Your number can also be written as,

$\implies \rm \frac { 1 } { 8^ \frac {1 } { 3 } }$

As sign of exponent changes when we reciprocate the base,

$\implies \rm \frac { 1 } { 2^{3 \frac {1 } { 3 } }}$

$\implies \rm \frac { 1 } { 2 }$

$\implies \rm 0.5$